Differential Equations

Let \(\alpha|x|=|y| \mathrm{e}^{x y-\beta}, \alpha, \beta \in \mathbf{N}\) be the solution of the differential equation \(x \mathrm{~d} y-y \mathrm{~d} x+x y(x \mathrm{~d} y+y \mathrm{~d} x)=0,y(1)=2\). Then \(\alpha+\beta\) is equal to ________